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Visual Interpretation (Multi/Ordinal)

🎯 Purpose

Use this visual guide to understand, validate, and communicate results from Multiclass (Nominal) and Ordinal Logistic Regression models. Each plot helps assess model behavior, class probability structure, and assumption alignment.

1️⃣ Multiclass (Multinomial Logistic Regression)

πŸ“ˆ A. Class Probability Distributions

What it shows: Predicted probability for each class per observation

import matplotlib.pyplot as plt
probs = model.predict_proba(X_test)
plt.plot(probs)
plt.title("Predicted Class Probabilities")

βœ”οΈ Helps detect low-confidence predictions or class overlap

What it shows: Influence of features on class probability scores

# Use partial dependence or coefficient plots per class

βœ”οΈ Visualizes how specific features shift class predictions

πŸ—‚ C. Confusion Matrix (Multiclass)

from sklearn.metrics import ConfusionMatrixDisplay
ConfusionMatrixDisplay.from_predictions(y_true, y_pred)

βœ”οΈ Detects which classes are often confused

2️⃣ Ordinal Logistic Regression

πŸ“Š A. Predicted Score Distributions by Class

What it shows: Where the model places predicted scores relative to ordinal thresholds

# After fitting ordinal model, visualize raw prediction scores by actual class
sns.violinplot(x=y_true, y=model.decision_function(X))

βœ”οΈ Look for monotonic separation between categories

πŸ“ B. Threshold Cutoffs

What it shows: Estimated logit cut points between ordinal levels

# Ordinal models like mord expose thresholds (intercepts)
print(model.intercept_)  # ΞΈ_j values

βœ”οΈ Check if spacing between cut points makes sense (e.g., large jump from β€˜medium’ to β€˜high’)

πŸ§ͺ C. Proportional Odds Diagnostic (Optional)

What it shows: If slopes are consistent across class splits

  • Fit parallel regressions across class thresholds
  • Plot coefficients or marginal effects by threshold group

βœ”οΈ If slopes differ greatly, PO assumption may be violated

βœ… Visual Interpretation Checklist

  • [ ] Class probabilities or scores plotted
  • [ ] Confusion matrix reviewed
  • [ ] Thresholds and score separations visualized (ordinal only)
  • [ ] Softmax/logit outputs mapped to interpretable odds
  • [ ] Assumptions flagged visually if violated

πŸ’‘ Tip

β€œIf your classes are confused or your thresholds overlap β€” it’s your visuals, not your coefficients, that will tell the truth.”